What this calculator does
Water potential determines which way water moves: always from higher potential to lower. Pure water at atmospheric pressure is defined as zero, and adding solute makes it negative, which is why a cell with a concentrated interior draws water in.
The total is the sum of two components. Solute potential is negative and comes from dissolved particles, calculated as −iCRT. Pressure potential is usually positive in a turgid plant cell, where the cell wall pushes back against the incoming water. A flaccid cell has a pressure potential of zero, which is the case this calculator defaults to.
The formula
Solute potential is minus the ionisation constant multiplied by molar concentration, the gas constant of 0.008314 L·MPa per mol·K, and absolute temperature in kelvin. Pressure potential is added to that to give total water potential. Temperature is entered in Celsius and converted to kelvin internally.
| Term | Meaning |
|---|---|
| Ψ (psi) | Total water potential in megapascals, the sum of the solute and pressure components. |
| Ψs | Solute potential, always negative or zero, from dissolved particles. |
| Ψp | Pressure potential, positive in a turgid cell and zero in a flaccid one. |
| i | Ionisation constant: 1 for a non-dissociating solute like sucrose, 2 for NaCl, which splits into two ions. |
The inputs explained
| Field | What to enter |
|---|---|
| Ionization constant i | The ionisation constant. Use 1 for sucrose and other non-ionising solutes, 2 for sodium chloride, 3 for calcium chloride. |
| Solute concentration (mol/L) | Molar concentration of the solution, in moles per litre. |
| Temperature (°C) | Temperature in degrees Celsius. |
| Pressure potential Ψp (MPa) | Pressure potential in MPa. Zero for an open solution or a flaccid cell, positive for a turgid one. |
When to use it
Predicting the direction of water movement
Comparing the potential of a cell against its surroundings answers whether water enters or leaves, which is the whole purpose of the quantity.
Working through a plant physiology problem
Textbook problems give concentration, temperature and sometimes pressure, and ask for the potential or for which way water moves. This is that calculation.
Understanding plasmolysis
A cell in a solution more concentrated than its interior loses water, the membrane pulls away from the wall and pressure potential falls to zero, which the arithmetic shows directly.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does solute concentration change water potential?
A range of molar concentrations with a non-ionising solute at room temperature.
| Concentration | Water potential Ψ | Solute potential Ψs | Temperature used |
|---|---|---|---|
| 0.1 M | -0.2479 MPa | -0.2479 MPa | 298.15 K |
| 0.3 M | -0.7436 MPa | -0.7436 MPa | 298.15 K |
| 0.5 M | -1.239 MPa | -1.239 MPa | 298.15 K |
| 1 M | -2.479 MPa | -2.479 MPa | 298.15 K |
Questions
Which way does water move?
From higher water potential to lower, always. Since pure water is zero and solutions are negative, water moves from dilute to concentrated. The numbers being negative makes this easy to get backwards: −0.2 MPa is higher than −2.0 MPa.
What is the ionisation constant for?
It counts the particles a solute produces in solution. Sucrose does not dissociate so i is 1. Sodium chloride splits into two ions so i is 2, making a 0.1 M NaCl solution twice as effective at lowering potential as 0.1 M sucrose. It is the number of particles that matters, not the number of formula units.
When is pressure potential not zero?
In a turgid plant cell, where the rigid wall resists the incoming water and generates positive pressure. It can also be negative, as in the xylem, where transpiration pulls water under tension. An open beaker of solution has a pressure potential of zero.
Why is water potential negative?
Because pure water at atmospheric pressure is defined as the zero point and adding anything to it lowers the potential. The scale is a convention, chosen so that the reference state is a round number, and the negative values simply reflect that almost every real solution sits below it.
For the atmospheric side of plant water demand, see the vapor pressure deficit calculator. For light availability, see the daily light integral calculator.